FATA: An Efficient Optimization Method based on Geophysics

Abstract: An efficient swarm intelligence algorithm, named the Fata Morgana Algorithm (FATA), is proposed to address continuous multi-type optimization problems. Inspired by the mirage formation process, FATA incorporates the Mirage Light Filtering Principle (MLF) and the Light Propagation Strategy (LPS). The MLF strategy, in conjunction with the definite integration principle, enhances FATA’s exploration capability, while the LPS strategy, combined with trigonometric principles, improves convergence speed and exploitation capability. These strategies optimize FATA's population and individual search abilities. FATA's performance is validated through comparisons with various competitive optimizers on 23 benchmark functions and IEEE CEC 2014, demonstrating its effectiveness in solving diverse functions. Additionally, FATA is tested on three practical engineering optimization problems, yielding superior results compared to other methods. The algorithm's potential as an efficient tool for practical optimization tasks is evident.

Fata Morgana Algorithm (FATA): The Fata Morgana Algorithm (FATA) is a novel optimization approach inspired by the natural phenomenon of mirages. It integrates local and global search strategies to tackle complex optimization problems efficiently. Below is an overview of the core components and mechanisms of FATA.

Conceptual Foundation: The core concept of FATA emulates the mirage formation process, where light rays undergo filtering, refraction, and reflection in an inhomogeneous medium. This principle is translated into an optimization framework to balance exploration and exploitation within the algorithm.

Algorithm Structure: FATA operates through several distinct phases:

Mirage Light Filtering Principle: This principle drives the population’s exploration capability by evaluating and filtering individuals based on the definite integral principle, aiming to enhance the algorithm’s global search performance.

Light Propagation Strategy: This strategy, inspired by the refraction and reflection of light, focuses on local exploitation. It includes first-half refraction, second-half refraction, and total internal reflection processes to refine solutions around the optimal.

Summary of FATA Stages: FATA incorporates the following key mechanisms:

The FATA algorithm begins with a random population and iteratively applies mirage light filtering and light propagation strategies to enhance exploration and exploitation. This process aims to balance global and local search capabilities, demonstrating FATA's potential as an effective optimization tool.